Press Release

Kamakura Chief Data Scientist Dr. Sou-Cheng T. Choi
and Team at Illinois Institute of Technology Announce
Software Release of Guaranteed Automatic Integration Library (GAIL), Version 2.3.1

The Guaranteed Automatic Integration Library (GAIL) research and development team in the Department of Applied Mathematics, at Illinois Institute of Technology (Illinois Tech) is pleased to announce the release of GAIL version 2.3.1 on Father's Day, June 21. The GAIL team members include Fred J. Hickernell (Illinois Tech), Sou-Cheng T. Choi (Kamakura Corporation and IIT), Yuhan Ding (Illinois Tech), Jagadeeswaran Rathinavel (Wi-Tronix, LLC), Xin Tong (University of Illinois, Chicago), Lluís Antoni Jiménez Rugama (UBS), Lan Jiang (Compass Inc.), Xuan Zhou (J.P. Morgan), and Yizhi Zhang (Jamran International Inc.). We are also thankful for contributions from our current students, Kan Zhang and Aleksei Sorokin.

GAIL is an open-source MATLAB library that implements our research on one- and multi-dimensional numerical integration; one-dimensional function approximation and global optimization on a finite domain. It is the fruition of our work over the past seven years since release of version 1.0 in 2013. All GAIL algorithms provide guarantees of accuracies based on robust theory. Each algorithm automatically estimates the required number of sampling points for meeting user-specified tolerances, and then returns solution estimates, error bounds, and other important information such as number of sampling points, run time, and warnings, whenever available.

Highlights of this release are two automatic Bayesian cubature methods, namely cubBayesLattice_g and CubBayesNet_g. They consider an integrand as a realization of a Gaussian process, and use lattice and Sobol points, respectively, for sampling purposes.

Source code, examples, demos, test cases, published papers, and software documentation of GAIL with current and past releases are available for free at All the materials are developed and tested in MATLAB versions R2016a to R2020a. We welcome collaboration, contributions, and comments from our users and scientific community members. The GAIL team can be reached at

Some of the GAIL algorithms are being actively ported to the Python 3 library, Quasi-Monte Carlo Community Software (QMCPy). For more details, please refer to the Apache QMCPy homepage at

Our work is based on research partially supported by the National Science Foundation under grants NSF-DMS-1522687 and NSF-DMS-1115392; and the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under contract DE-AC02-06CH11357.

About Kamakura Corporation
Founded in 1990, Honolulu-based Kamakura Corporation is a leading provider of risk management information, processing, and software. Kamakura was recognized as a category leader in the Chartis Report, Technology Solutions for Credit Risk 2.0 2018. Kamakura was named to the World Finance 100 by the editor and readers of World Finance magazine in 2017, 2016 and 2012. In 2010, Kamakura was the only vendor to win two Credit Magazine innovation awards. Kamakura Risk Manager, first sold commercially in 1993 and now in version 10.1, is the first enterprise risk management system for users focused on credit risk, asset and liability management, market risk, stress testing, liquidity risk, counterparty credit risk, and capital allocation from a single software solution. The KRIS public firm default service was launched in 2002. The KRIS sovereign default service, the world’s first, was launched in 2008, and the KRIS nonpublic firm default service was offered beginning in 2011. Kamakura added its U.S. Bank default probability service in 2014.

Kamakura has served more than 330 clients with assets ranging in size from $1.5 billion to $3.0 trillion. Current clients have a combined “total assets” or “assets under management” in excess of $26 trillion. Its risk management products are currently used in 47 countries, including the United States, Canada, Germany, the Netherlands, France, Austria, Switzerland, the United Kingdom, Russia, Ukraine, South Africa, Australia, China, Hong Kong, India, Indonesia, Japan, Korea, Malaysia, Singapore, Sri Lanka, Taiwan, Thailand, Vietnam, and many other countries in Asia, Europe and the Middle East.

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